\[\boxed{\mathbf{468}.}\]
\[1)\ a^{\frac{1}{4}} = \sqrt[4]{a};\]
\[2)\ b^{\frac{3}{5}} = \sqrt[5]{b^{3}};\]
\[3)\ a^{- \frac{5}{6}} = \sqrt[6]{a^{- 5}};\]
\[4)\ b^{- \frac{1}{3}} = \sqrt[3]{b^{- 1}};\]
\[5)\ (2y)^{\frac{1}{3}} = \sqrt[3]{2y};\]
\[6)\ (5b)^{- \frac{3}{4}} = \sqrt[4]{(5b)^{- 3}}.\]